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Outline• Introduction to Convolutional Encoders• Circuit Diagrams• State Diagrams• Trellis Diagrams1Block Codes — Review• Encoder for an (n, k) block code C:u[1], u[2], . . . →Encoder→ x[1], x[2], . . . .• Here u[1], u[2], . . . is a sequence of k-dimensional infor-mation blocks of length k, and x[1], x[2], . . . is the corre-sponding sequence of n-dimensional code blocks wherex[i] = u[i]G,G being a k × n generator matrix for C.2An (n, k, m) Convolutional Encoder• (There is an m-dimensional memory register inside.)• m = 0 corresponds to a block code.• Conclusion? A block code is a special case of a convolu-tional code.3Example 1: A (2, 1, 2) Convolutional Encoder• (2, 1) block codes are trivial.4From Circuit Diagram to State Diagram5From State Diagram to Trellis Diagram6The Truncated Trellis• This is a (14, 5) block code!• Or rather, a nonsystematic encoder for a (14, 5) blockcode.7Conclusion?• A convolutional code is a special kind of block


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CALTECH EE 127 - Lecture notes

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